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Articles 3601 - 3630 of 4002

Full-Text Articles in Systems Science

Predator-Prey Dynamics-Based Optimization, Qiuqin Lu, Guangqiu Huang Jan 2019

Predator-Prey Dynamics-Based Optimization, Qiuqin Lu, Guangqiu Huang

Journal of System Simulation

Abstract: To solve the complex function optimization problem, a predator-prey dynamics optimization algorithm is proposed. The algorithm assumes that there are two species of predator and prey in an ecosystem. There is competition among the same species, the higher the population density, the more intense the competition, and then characteristics of populations are more likely to produce changes; strong populations are more likely to defeat weak populations when competition, and thus to obtain significant changes in their own characteristics. When predator populations eat prey populations, their characteristics also change. The competition operator, the predator-prey operator and the growth operator are …

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Extensible Battle Management Ontology Language, Zaijiang Tang, Xiangzhong Xue, Xue Qin Jan 2019

Extensible Battle Management Ontology Language, Zaijiang Tang, Xiangzhong Xue, Xue Qin

Journal of System Simulation

Abstract: The interoperability of command and control system with combat simulation system is an important and difficult problem in the construction of practical training environment. Aiming at the existing problems of semantic interoperability of language description, the battle management language, web ontology language and extensible markup language are studied. Based on ontology theory, the extensible battle management ontology language (XBMOL) is proposed. The syntax structure and semantic annotation of XBMOL are analyzed as an extension to the C-BML. The XBMOL 6W1H architecture is designed, and the extensible grammatical structure and semantic tagging are described. An example with XBMOL is given …

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Service Recommended Trust Algorithm Based On Cloud Model Attributes Weighted Clustering, Jindong Wang, Zhiyong Yu, Hengwei Zhang, Fang Chen Jan 2019

Service Recommended Trust Algorithm Based On Cloud Model Attributes Weighted Clustering, Jindong Wang, Zhiyong Yu, Hengwei Zhang, Fang Chen

Journal of System Simulation

Abstract: In cloud computing, there are cloud services of different qualities. How to choose credible and reliable service has become a key issue when users select services. Aiming at the shortcomings of the existing evaluation methods, a service clustering method based on attributes weighted cloud model is proposed. The users’ evaluation similarity with weighted Pearson correlation coefficient method based on service clustering is calculated. The users’ similarity combined with the index weights of users’ service selection is computed. The nearest neighbors are gotten. The recommendation trust of the services with the recommendation trust algorithm is obtained. Simulation results …

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Indoor Positioning Algorithm Based On Zigbee And Improved Radio Frequency Identification, Dahu Yan, Yangjie Xu Jan 2019

Indoor Positioning Algorithm Based On Zigbee And Improved Radio Frequency Identification, Dahu Yan, Yangjie Xu

Journal of System Simulation

Abstract: Since the traditional RFID positioning technology relies on the Internet and is especially constrained by the positioning distance in the process of positioning the tags with poor positioning accuracy, a novel positioning algorithm is proposed based on the ZigBee and improved VIRE algorithm. By using the proposed algorithm, ZigBee nodes are adopted to achieve the formation of network information transmission to replace the traditional wired communication. Gaussian-Kalman filter is used to deal with the sampling data of the limited preselected reference node signal strength. The algorithm adopts signal propagation loss model to calculate the RSSI values of virtual reference …

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Modeling And Simulation Of Missile Defense M/M/N Queueing System, Longyue Li, Fuxian Liu, Huizhen Zhao Jan 2019

Modeling And Simulation Of Missile Defense M/M/N Queueing System, Longyue Li, Fuxian Liu, Huizhen Zhao

Journal of System Simulation

Abstract: To simulate the process of ballistic missile defense and to study the effectiveness of defense, the M/M/N queueing system of missile defense was modeled and simulated. A queueing modeling framework was given to explain the meaning and distribution of related parameters. The M/M/N/N and M/M/N/C queueing models were proposed for short defense depth and long defense depth respectively, and the single target channel and the multiple target channels were distinguished in each model. How to deal with the different types of missile defense system based on equivalent replacement method were also considered. Simulation examples verified the main …

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De-Noising Method Of Eeg Signal Based On Mmtd And Wavelet Hard-Threshold, Guoqiang Yan, Ningning Zhou, Shaobai Zhang Jan 2019

De-Noising Method Of Eeg Signal Based On Mmtd And Wavelet Hard-Threshold, Guoqiang Yan, Ningning Zhou, Shaobai Zhang

Journal of System Simulation

Abstract: To overcome the shortage of losing partial important information of hard-threshold method with EEG signal de-noising process, a novel de-noising method based on the combination of measuring of medium truth degree (MMTD) and EEG is proposed. By decomposing noisy signals of wavelet transform, handling threshold of high-frequency wavelet coefficients in every layer, and reconstructing post-processing of the wavelet coefficients, the purpose of noise elimination can be guaranteed. Under different noise intensity, the experimental results show that the MAWH (MMTD and wavelet hard-threshold) method has perspective of lower RMSE and higher SNR compared to hard-threshold and soft-threshold.

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Satisfactory Fault-Tolerant Control Of Nncs Under Event-Triggered Sparse Data Transmission, Yajie Li, Li Wei Jan 2019

Satisfactory Fault-Tolerant Control Of Nncs Under Event-Triggered Sparse Data Transmission, Yajie Li, Li Wei

Journal of System Simulation

Abstract: Adopting the discrete event-triggered communication scheme (DETCS), the satisfactory fault-tolerant control of nonlinear networked control system (NNCS) under the sparse data transmission circumstance was studied. Based on the background of event-triggered sparse data transmission, a closed-loop model with actuator failure and actuator saturation was established. Based on Lyapunov-Krasovskii function and the safety degree definition proposed in this paper, a sufficient condition was presented for NNCS with the generalized H?/H2 performance under the case of actuator saturation and actuator failure, which was the contractively invariant set of fault-tolerance with α-safety degree, and …

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Soft Shadow Rendering Algorithm Based On Gpu’S Shadow Line, Shanxiao Gao, Wu Xian Jan 2019

Soft Shadow Rendering Algorithm Based On Gpu’S Shadow Line, Shanxiao Gao, Wu Xian

Journal of System Simulation

Abstract: To solve the problem of soft shadow rendering algorithm on shaded body surfaces, a new algorithm based on shadow lines which can render better soft shadow with less cost computation overhead is presented. GPU is used to create shadow lines which include starting point, ending point and shading value. The computer shader (CS) is used to amend the shading value by inverse distance weighting function. In the phase of shadow rendering, the shadow lines dataset is used to calculate the current pixel's shading value by trigonometric interpolation. Experimental result shows that the algorithm can solve the soft shadow …

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Modeling And Simulation On Delay Of Central Heating System For Temperature Prediction, Sun Tao, Shaoxiong Ji Jan 2019

Modeling And Simulation On Delay Of Central Heating System For Temperature Prediction, Sun Tao, Shaoxiong Ji

Journal of System Simulation

Abstract: Heating prediction is essential for energy saving. However, it is difficult to some extent because the central heating system (CHS) is nonlinear with large-scaled delay and other characteristics. Based on physical laws of the CHS, a novel model combining pruning algorithm with the least mean square is proposed to solve the problem of delay and predict the temperature. The model with the delay taking into consideration conforms to the law of thermal transmission. The pruning algorithm lowers the computational complexity. Simulations using gradient descent least squared regression (LSR), support vector machine (SVM), least-squared support vector machine (LS-SVM) …

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Simulation Of Two Stages-Variant Growth Evolution Model Of High-Speed Railway And Civil Aviation Compound Network, Xu Feng, Jinfu Zhu, Jianjun Miao, Rongrong Ding Jan 2019

Simulation Of Two Stages-Variant Growth Evolution Model Of High-Speed Railway And Civil Aviation Compound Network, Xu Feng, Jinfu Zhu, Jianjun Miao, Rongrong Ding

Journal of System Simulation

Abstract: Combining the special evolving characteristics of the high-speed railway and civil aviation compound network, an evolution model which has two stages with variant growth mechanism and variable parameters is constructed, and the rationality of the model is verified through mathematical simulation. The model divides the evolutionary process into two stages: the stage of single-point growth pattern, and the stage of variant and alternant growth pattern. The probability of two sub-networks’ random and commutative growth could be controlled by changing the parameters’ values, and then the evolving rhythm and scale of the compound network could be adjusted. The simulation results …

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Flow Field Analysis Of Pipeline Pig Receiving Trap, Chuanjun Han, Yu Cheng, Xingzhi Duan, Li Qi Jan 2019

Flow Field Analysis Of Pipeline Pig Receiving Trap, Chuanjun Han, Yu Cheng, Xingzhi Duan, Li Qi

Journal of System Simulation

Abstract: To study the influence of piping diameter on the flow field characteristics when pig receiving trap is working, the finite element model of pig receiving trap whose type is P6.3MPa DN700/DN600 was established, and the effects of the diameters changes of vent pipe and blow-off pipe were simulated. The effects caused by the pig running speeds on the flow field of the pig receiving trap were studied. The results show that in the pig receiving trap, there is the maximum pressure in the left side of pig staying and the pressure begins to decrease and easy to form swirls …

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Elevator Traffic Pattern Recognition With Fcm Clustering Based Fuzzy Neural Network, Zhenshan Yang, Wenjiao Yue Jan 2019

Elevator Traffic Pattern Recognition With Fcm Clustering Based Fuzzy Neural Network, Zhenshan Yang, Wenjiao Yue

Journal of System Simulation

Abstract: Elevator traffic demand pattern recognition is the prerequisite for effectively implementing the strategies of elevator group control system. In view of the characteristics of time-varying, nonlinear and uncertainty of elevator traffic demand, an elevator traffic pattern recognition method with FCM (Fuzzy C-means) clustering based fuzzy neural network is presented. The method introduces the fuzzy logic into the calculation and learning of BP neural network, and employs FCM clustering algorithm to cluster the original traffic demand to realize the fuzzy partition of the input space of fuzzy system to determine the initial value of network membership function and clustering center …

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Application Of Multiple-Stepwise And Kalman Filtering In Haze Forecast, Yunhao Xian, Hengde Zhang, Yonghua Xie, Le Yang Jan 2019

Application Of Multiple-Stepwise And Kalman Filtering In Haze Forecast, Yunhao Xian, Hengde Zhang, Yonghua Xie, Le Yang

Journal of System Simulation

Abstract: Considering the importance of objective haze forecast and the low accuracy rate of haze forecast, a new haze objective forecast correction method based on the multiple stepwise regression algorithms and the Kalman filtering algorithm is proposed. The multiple stepwise regression method is used to control the physical factor of the dependent variable, and the visibility forecast equation is established. The Kalman filtering method is adopted to correct the regression coefficient in multivariate stepwise regression algorithm according to the actual data, and the haze objective forecast correction model is established. The experiments are carried out in Beijing, Guangzhou, Nanjing and …

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Finite Element Analysis Of Magnetic Flux Leakage Detection For Transverse Cracks Of Sucker Rod, Zhang Ou, Xueye Wei, Wang Pei, Shuxin Yan Jan 2019

Finite Element Analysis Of Magnetic Flux Leakage Detection For Transverse Cracks Of Sucker Rod, Zhang Ou, Xueye Wei, Wang Pei, Shuxin Yan

Journal of System Simulation

Abstract: The modeling and testing technology of the surface transverse cracks of complex defecting for sucker rod were studied, and a finite element simulation model of rod transverse defects was built. The magnetic flux leakage testing simulation was carried out by using ANSYS software, and the changing trend between the lift-off value and the leakage magnetic field was obtained. Two kinds of different magnetization modes of single coil and double coils were analyzed, and the result showed that the double coils magnetization is superior to single coil magnetization. The two dimensional and three dimensional magnetic flux leakage testing …

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Counterforce Characteristics Of Shrapnel In Magnetic Latching Relay Based On Abaqus, Xiuping Su, Jiaying Dong, Yanhua Qiao, Huang Min Jan 2019

Counterforce Characteristics Of Shrapnel In Magnetic Latching Relay Based On Abaqus, Xiuping Su, Jiaying Dong, Yanhua Qiao, Huang Min

Journal of System Simulation

Abstract: A 3D model of contact system in magnetic latching relay was established by the software Pro/E, and the shrapnel deformation by force was analyzed in the contact system using finite element analysis software Abaqus. The advantages of Abaqus software in the multibody system simulation were analyzed and summarized, a modeling and simulation approach to contact multibody system in magnetic latching relay based on Abaqus was proposed. The selection of element type, technology of mesh division, definition of boundary condition, and establishment of finite element model were studied. The non-convergence problems were solved in the simulation analysis by adding binding …

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Optimal Operation Of Grid-Connected Microgrid Based On Abc Algorithm, Qiuli Cui Jan 2019

Optimal Operation Of Grid-Connected Microgrid Based On Abc Algorithm, Qiuli Cui

Journal of System Simulation

Abstract: An optimal scheduling model of grid-connected microgrid composed of wind power generators, photovoltaic cells, fuel cells and batteries is established. The economy and environmental protection elements are considered in this model. To maximize the role of peak shaving and valley filling in microgrid system, based on the time-of-use price mechanism, the heuristic rules combined with peak shaving and valley filling is used to design a grid-connected energy scheduling strategy. By monitoring the net load state and the price time interval, and adjusting the particular state of the micro source of power, the system optimal energy scheduling state is obtained. …

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Power Control Algorithm Based On Non-Cooperative Game Theory Of Wbans, Xu Yong, Mengya Ke, Fen Liu, Qianming Zha Jan 2019

Power Control Algorithm Based On Non-Cooperative Game Theory Of Wbans, Xu Yong, Mengya Ke, Fen Liu, Qianming Zha

Journal of System Simulation

Abstract: A non-cooperative self-adaptive power control algorithm is proposed based on the model of TDMA wireless body area networks (WBANs) interference. The algorithm is put forward using payoff function and cost function as utility functions.The transmitting power vector is obtained by the optimal response strategy update. It is proved that the network can reach Nash Equilibrium with the transmitting power vector, and in this situation all the users’ utility function is maximized. The Matlab is applied to simulation process of the algorithm, during which simulation has been carried out with different parameters. Compared with …

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Aerodynamic Noise Generating Mechanism Of Corbula Type Throttle Valves, Yueqin Li, Xiao Fei, Fan Ming, Xiaodong Xu Jan 2019

Aerodynamic Noise Generating Mechanism Of Corbula Type Throttle Valves, Yueqin Li, Xiao Fei, Fan Ming, Xiaodong Xu

Journal of System Simulation

Abstract: The throttle mechanism of pneumatic noise and the noise spectrum characteristics of corbula type throttle valve are studied by targeting on aerodynamic noise problems caused by gas when flowing through the corbula type throttle valve, the method of CFD software with acoustic software simulationis used as well. The studies have showed that when the flow of fluid flows through shrink section, it can be effected by throttling effect, the speed of gas on the hole exit increases rapidly to form under-expanded supersonic jet, causing strong turbulence and shock wave noise. The conclusionis that the construction of throttling …

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Research On Network Public Opinion Simulation From Interdisciplinary Perspective, Lingnan He, Kaisheng Lai, Zhongxuan Lin, Xiling Xiong Jan 2019

Research On Network Public Opinion Simulation From Interdisciplinary Perspective, Lingnan He, Kaisheng Lai, Zhongxuan Lin, Xiling Xiong

Journal of System Simulation

Abstract: The simulation of network public opinion shows a trend of interdisciplinary development. On the one hand, the method of data analysis in network public opinion belongs to natural science; on the other hand, participants are social people and have strong social scientific attributes. However, at present, most of the simulation models come from the natural science fields such as system dynamics, Markov model, small-world theory and SIS model, etc. This paper introduces the big five personality of psychology, media literacy of communication, opinion leaders and diffusion of innovation theory, taking the psychological modeling in the dissemination of the main …

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Dynamic Data Modeling Driven Model For Forest Fire Spread Based On Devs, Guoxiong Zhou, Kejia Yin, Aibin Chen Jan 2019

Dynamic Data Modeling Driven Model For Forest Fire Spread Based On Devs, Guoxiong Zhou, Kejia Yin, Aibin Chen

Journal of System Simulation

Abstract: According to the characteristics of fire behavior with strong sudden, disposal of difficult rescue, and heavy destructiveness, combining dynamic data system and discrete event system specification model, a dynamic data driven forest fire spread model is put forward based on devs modeling. The dynamic data system needs to be realized through the interaction between the computer software and the data characteristics of each environment, which is characterized by flexible data and real data. DEVS supports object-oriented modeling, and can make the modeling and simulation of the system modular, hierarchical and formal. The model is set up according to the …

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Study On Evacuation Modeling Of Airport Based On Social Force Model, Shaobo Zhong, Zhichen Yu, Yongsheng Yang, Sun Chao, Quanyi Huang Jan 2019

Study On Evacuation Modeling Of Airport Based On Social Force Model, Shaobo Zhong, Zhichen Yu, Yongsheng Yang, Sun Chao, Quanyi Huang

Journal of System Simulation

Abstract: Public safety events frequently occurred in China and caused great casualty and property loss. Inefficient evacuation is one of the major causes of casualties in emergencies. Taking the T3-E of the Beijing Capital International Airport as a study area, the influence of four factors of evacuation guidance, customs barriers, the airport seats, and construction columns studies is studied through social force model-based simulation. The results show that: four factors have local effects on evacuation respectively. Evacuation guidance has the most significant positive effect while others have a little significant negative effect. Moreover, the relationships between the maximal and optimal …

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Application Of Compound Control For Flight Simulator With Eid Estimator, Ren Yan, Guanhua Zhao, Wenbo Tan, Xiaodong Liu Jan 2019

Application Of Compound Control For Flight Simulator With Eid Estimator, Ren Yan, Guanhua Zhao, Wenbo Tan, Xiaodong Liu

Journal of System Simulation

Abstract: In view of the problem that the interference and nonlinear friction sensitively effect on flight simulators, an improved approximation differential compound control strategy with Equivalent Input Disturbance (EID) estimator is presented. Moreover, the setting conditions based on given parameters was proposed. In the presented strategy, the EID estimator can compensate the equivalent input disturbance of the system. Furthermore, owing to the construction of the digital feedforward via the improved differentiator, the improved approximation differentiator is able to acquire accurately the velocity and the acceleration of the signal, and has an ability to inhibit the partial noise by use of …

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Visual Simulation Of Aircraft Approach And Landing System Based On Beidou, Ruihua Liu, Cao Hui Jan 2019

Visual Simulation Of Aircraft Approach And Landing System Based On Beidou, Ruihua Liu, Cao Hui

Journal of System Simulation

Abstract: In order to analyze the navigation performance of Ground-Based Augmentation System (GBAS) based on Beidou satellite navigation system (BDS) in approach and landing phase, segments of ground, airborne and space were simulated as GBAS. The broadcast ephemeris data was processed by MATLAB to simulate the BDS constellation and the orbit operation. Based on the minimum operational standards for GBAS released by RTCA, the data model of ground segment and airborne segment were established, and the enhancement algorithm was simulated to analyze the positioning error and navigation performance of BDS. Simulink kinematic and control models were developed to simulate the …

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Research On Sensorless Control Method Based On Improved Kalman Filter Of Sliding Mode Observer, Haigang Zhang, Yuanyuan Nie, Zhang Lei, Bulai Wang, Yinzhong Ye, Wan Heng Jan 2019

Research On Sensorless Control Method Based On Improved Kalman Filter Of Sliding Mode Observer, Haigang Zhang, Yuanyuan Nie, Zhang Lei, Bulai Wang, Yinzhong Ye, Wan Heng

Journal of System Simulation

Abstract: Aiming at problems of high frequency ripple component existed in PMSM parameter error caused by the sliding mode observer (SMO) estimation error and counter electromotive force, the stable condition of the speed sensorless control system of permanent magnet motor is weakened. The Kalman filter is introduced to eliminate the high frequency ripple in the front of the sliding mode observer. The control system of the permanent magnet synchronous motor has better steady-state effect and dynamic response. A Matlab platform has been built to validate this method, the experimental results show that the improved sliding mode observer is strong …

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Multiple Objective Planning Of Distribution Network With Multiple Distributed Generations, Pan Huan, Xu Chen, Yang Li Jan 2019

Multiple Objective Planning Of Distribution Network With Multiple Distributed Generations, Pan Huan, Xu Chen, Yang Li

Journal of System Simulation

Abstract: The types of distribution network with Distributed generations (DG), the location and capacity will impact on power grid operation and strict, such as unreasonable planning, the normal operation of the power grid have negative effects. Based on this, the main purpose of this paper is to study when the new DG of distribution network access how to reasonable siting and sizing, specific arrangements are. To a real distribution system with a region as an example, the node were evaluated to determine candidate DG installation node, corresponding mathematical optimization model is established, in distribution power purchasing cost, DG operation and …

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Research On Mode Shape Characteristics Simulation Of Bell-Shaped Vibratory Angular Rate Gyro, Liu Ning, Su Zhong Jan 2019

Research On Mode Shape Characteristics Simulation Of Bell-Shaped Vibratory Angular Rate Gyro, Liu Ning, Su Zhong

Journal of System Simulation

Abstract: It presents the analysis method of metal shell vibratory gyro’s mode shape for simulation research on Bell-shaped vibratory angular rate gyro, and gives the solution process and result of simulation analysis. Based on the Kirchhoff-Love assuming, by numerical methods to solve mode shape functions of bell-shaped resonator, the low-order modes of bell-shaped resonator is given through comprehensive analysis and finite element simulation results. The mode shaped characteristics of bell-shaped resonator is analyzed effectively through this method. Theory and simulation methods verify the correctness of the theory and promote modal, and lay the bell-shaped vibratory angular rate gyro …

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Key Points Analysis And Simulation For Sea Surface Velocity Estimation Based On Spaceborne Ati-Sar System, Yan He, Daiyin Zhu Jan 2019

Key Points Analysis And Simulation For Sea Surface Velocity Estimation Based On Spaceborne Ati-Sar System, Yan He, Daiyin Zhu

Journal of System Simulation

Abstract: ATI (Along Track Interferometric) technique is one of the most important applications for spaceborne SAR (Synthetic Aperture Radar) systems. ATI-SAR systems can directly detect the Doppler offset associated with each pixel of a SAR image. This is achieved by interferometric combination of two complex SAR images of the same scene. The sea surface velocity can be estimated via the calculated interferometric phase. The baseline length, velocity resolution and velocity estimation error are three important factors in the process of spaceborne ATI-SAR system design, and these three points are carefully investigated here. The basic principle and expression of spaceborne ATI-SAR …

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Economic Design Of Vsi Arma Charts, Zhang Li, Xiaoyang Dong Jan 2019

Economic Design Of Vsi Arma Charts, Zhang Li, Xiaoyang Dong

Journal of System Simulation

Abstract: To improve the sensitivity of statistical process control reducing costs for process monitoring at the same time, the economic design of autoregressive moving average control chart with variable sampling interval (VSI ARMA) was discussed. The economic model of autoregressive moving average control chart with variable sampling interval (VSI ARMA) was established based on Lorenzen and Vance’s model, in which Markov chain was used to calculate the average time to signal (ATS) through constructing a three dimensional random vector. Using genetic algorithm to search for the optimal combination of seven parameters of VSI ARMA model made the cost of …

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Electromagnetic Property Of Axial Piston Pump/Motor Magnetic Slipper Pair, Haishun Deng, Xu Pan, Huang Ran, Yuefei Deng, Dai Peng Jan 2019

Electromagnetic Property Of Axial Piston Pump/Motor Magnetic Slipper Pair, Haishun Deng, Xu Pan, Huang Ran, Yuefei Deng, Dai Peng

Journal of System Simulation

Abstract: In order to control the oil film for the slipper pair more conveniently and flexibly, the magnetic slipper pair is proposed which maintains balance by hydraulic pressure and electromagnetic force, and its mathematical model and finite element model are built. The impact of voltage, electric field strength etc. on magnetic slipper pair’s working performance and service life is analyzed. The results show that: the position of the swash plate in contact with the core of magnetic slipper pair has maximum electric field strength and prone to discharging electric which affect the service life. The main magnetic path forms a …

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Study On How To Design Simplest Chaotic Circuit With Two Charge-Controlled Memristors, Shuhua Wu, Xuwei Rong, Zhenyong Liu Jan 2019

Study On How To Design Simplest Chaotic Circuit With Two Charge-Controlled Memristors, Shuhua Wu, Xuwei Rong, Zhenyong Liu

Journal of System Simulation

Abstract: A simplest five-order chaotic circuit is designed with two HP laboratory charge-controlled memristor models and its basic dynamic characteristics are studied using the conventional dynamic analysis method, through which its initial unstable oscillation is discovered and the initial oscillation process is recorded with the maximum Lyapunov exponent; the volt-ampere characteristic and the power output of the two memristors in the circuit are computed, indicating that the memristors are passive components; and the impacts of the inductance, capacitance and conductance to the circuit system are studied using the bifurcation diagram and the maximum Lyapunov exponent spectrum. In addition, the distribution …

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